Finite Group Databasebeta

← #35314992

Subgroups — #35314992

Order 21248.

464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24911771C211yesmaximal, characteristic
2C4×#14581709C211yesmaximal, characteristic
3#24905470C214yesmaximal, complemented
4C83×#1465C211yesmaximal, characteristic
5C2×#14581773—21no—
6C22×C4⋊Dic83C411yescharacteristic
7C2×#14581709—21no—
8C4×#13050574—21no—
9#19127631C2212yes—
10#19127626C412yes—
11#19127599—21no—
12#19127562—21no—
13#19127561—21no—
14#19127561C411yescharacteristic
15#19127470C2212yes—
16C2×C4×D4×C83C2211yescharacteristic
17#407×C83—21no—
18#324×C83C2212yes—
19#323×C83—21no—
20C23×Dic83—21no—
21C2×#13050574—22no—
22#14581773—44no—
23C2×C4⋊Dic83—21no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—41no—
26C2×C4⋊Dic83—41no—
27C2×C4⋊Dic83C2×C412yes—
28C2×Dic83⋊C4—22no—
29C2×C22⋊Dic83—22no—
30C2×C22⋊Dic83—21no—
31#14581709—24no—
32#14581703—41no—
33C4×C83⋊C8—41no—
34C83⋊#95—22no—
35C83⋊#95—22no—
36C83⋊#95C2×C412yes—
37C22×D4×C83D411yescharacteristic
38C23×C4×C83C2×C411yescharacteristic
39C23×C4×C83D411yescharacteristic
40C2×M16×C83—41no—
41C4×D4×C83—41no—
42C4×D4×C83—41no—
43C2×C4⋊C4×C83C2311yescharacteristic
44C2×C22⋊C4×C83C2×C411yescharacteristic
45C2×C22⋊C4×C83D411yescharacteristic
46C2×C42×C83D411yescharacteristic
47C22⋊C8×C83—22no—
48C22⋊C8×C83—41no—
49C22×Dic83—22no—
50C22×Dic83—22no—
51C22×Dic83—42no—
52C22×Dic83—42no—
53C22×Dic83—42no—
54#13050574—24no—
55#13050574—42no—
56C2×C83⋊C8—42no—
57C4⋊Dic83—42no—
58C4⋊Dic83—41no—
59C4⋊Dic83—41no—
60C4⋊Dic83—42no—
61Dic83⋊C4—44no—
62C22⋊Dic83—42no—
63C22⋊Dic83—44no—
64C24×C83C22⋊C411yescharacteristic
65C24×C83C22⋊C411yescharacteristic
66C2×D4×C83—22no—
67C2×D4×C83—22no—
68C2×D4×C83—41no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83—42no—
74C22×C4×C83—42no—
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80M16×C83—82no—
81C2×C8×C83—42no—
82C4⋊C4×C83—41no—
83C22⋊C4×C83—41no—
84C22⋊C4×C83—41no—
85C42×C83—21no—
86C42×C83—21no—
87C23×C83—21no—
88C23×C83—21no—
89C23×C83—21no—
90C23×C83—21no—
91C23×C83—21no—
92C23×C83—41no—
93C23×C83—41no—
94C23×C83—41no—
95C23×C83—41no—
96C23×C83#10412yes—
97C23×C83C2×C22⋊C411yescharacteristic
98D4×C83—44no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—22no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—42no—
106C2×C4×C83—42no—
107C2×C4×C83—42no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—81no—
112C2×C4×C83#9911yescharacteristic
113C2×C4×C83#9911yescharacteristic
114C2×C4×C83AGL(1,ℤ/8)12yes—
115C2×Dic83—42no—
116C2×Dic83—42no—
117C2×Dic83—42no—
118C2×Dic83—42no—
119C2×Dic83—42no—
120C2×Dic83—42no—
121C2×Dic83—84no—
122C8×C83—82no—
123C83⋊C8—44no—
124C22×C83—21no—
125C22×C83—21no—
126C22×C83—22no—
127C22×C83—42no—
128C22×C83—42no—
129C22×C83—42no—
130C22×C83—41no—
131C22×C83—41no—
132C22×C83—41no—
133C22×C83—41no—
134C22×C83—41no—
135C22×C83—81no—
136C22×C83C2×#9911yescharacteristic
137C22×C83#41811yescharacteristic
138C22×C83C2×#10411yescharacteristic
139C4×C83—21no—
140C4×C83—22no—
141C4×C83—41no—
142C4×C83—41no—
143C4×C83—41no—
144C4×C83#35212yes—
145Dic83—82no—
146Dic83—82no—
147#11780—831nomaximal, Sylow
148C2×C83—21no—
149C2×C83—21no—
150C2×C83—42no—
151C2×C83—81no—
152C2×C83#150711yescharacteristic
153C2×C83C2×#35211yescharacteristic
154C2×C83#213511yescharacteristic
155#2486—831no—
156C4×#100—831no—
157#1465D8311yescharacteristic
158#1346—834no—
159C83#1178011yescharacteristic, complemented, Sylow
160C2×#123—1661no—
161C2×C4×D4C2×D8311yescharacteristic
162C22×C4⋊C4—831no—
163C2×#100—1661no—
164#407—21no—
165C4×M16—1661no—
166#398—832no—
167#397—832no—
168#389—1661no—
169#381—1661no—
170#380—831no—
171#380—1661no—
172#343—832no—
173#324C2×D8312yes—
174#323—21no—
175C22×D4D33211yescharacteristic
176C23×C4—1661no—
177C23×C4C4×D8311yescharacteristic
178C23×C4C22⋊D8311yescharacteristic
179C2×M16—41no—
180C2×M16—1662no—
181#123—3324no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—3321no—
185C2×C4⋊C4—3321no—
186C2×C4⋊C4—832no—
187C2×C4⋊C4—1661no—
188C2×C4⋊C4—1661no—
189C2×C4⋊C4—1662no—
190C2×C4⋊C4C22×D8311yescharacteristic
191C2×C22⋊C4—1661no—
192C2×C22⋊C4—1662no—
193C2×C22⋊C4C4×D8311yescharacteristic
194C2×C22⋊C4C22⋊D8311yescharacteristic
195C2×C42D33211yescharacteristic
196#100—1664no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199#97—3321no—
200C4×C8—3321no—
201#95—832no—
202#95—1662no—
203#95—1662no—
204C24(C2×D83)⋊C411yescharacteristic
205C24(C2×D83)⋊C411yescharacteristic
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—3322no—
216C22×C4—3322no—
217C22×C4—3322no—
218C22×C4—1662no—
219C22×C4—1662no—
220C22×C4(C2×D83)⋊C411yescharacteristic
221C22×C4(C2×D83)⋊C411yescharacteristic
222C22×C4C2×C4×D8311yescharacteristic
223C22×C4C2×C22⋊D8311yescharacteristic
224C22×C4C2×D33211yescharacteristic
225M16—82no—
226M16—3322no—
227M16—1664no—
228C2×C8—42no—
229C2×C8—3322no—
230C4⋊C4—41no—
231C4⋊C4—3322no—
232C4⋊C4—3322no—
233C4⋊C4—3324no—
234C4⋊C4—3321no—
235C4⋊C4—3321no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—3322no—
239C22⋊C4—3324no—
240C42—21no—
241C42—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#1458171812yes—
252C23C2×(C2×D83)⋊C411yescharacteristic
253D4—44no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—3322no—
268C2×C4—3322no—
269C2×C4—3322no—
270C2×C4—3322no—
271C2×C4—3322no—
272C2×C4—3322no—
273C2×C4—6644no—
274C2×C4#1458170611yescharacteristic
275C2×C4#1458170611yescharacteristic
276C2×C4#1458182012yes—
277C8—82no—
278C8—3324no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22C2×#1458170611yescharacteristic
292C22#1912770711yescharacteristic
293C22C2×#1458171811yescharacteristic
294C4—21no—
295C4—22no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—6642no—
300C4—6642no—
301C4#1912749012yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2#2490598011yescharacteristic
307C2C2×#1912749011yescharacteristic
308C2#2490915711yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1465C2
socleC22×C83C2×#99
prime radicalC22×D4×C83D4
cosocleC2×C4⋊C4×C83C23
hypercenter#1465D83
hypocenterC83#11780
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #24905470C2semidirect
159. C83#11780semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249117712
C4×#145817092
#249054702
C83×#14652
#1178083